Optical Coherence Tomography—principles And Applications

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INSTITUTE OF PHYSICS PUBLISHINGREPORTS ON PROGRESS IN PHYSICSRep. Prog. Phys. 66 (2003) 239–303PII: S0034-4885(03)18703-9Optical coherence tomography—principles andapplicationsA F Fercher1 , W Drexler1 , C K Hitzenberger1 and T Lasser21Institute of Medical Physics, University of Vienna, Waehringer Strasse 13, A-1090 Wien,Austria2Laboratoire d’optique biomédicale, Institut d’imagerie et optique appliquée, EPFLLausanne, CH-1015 Ecublens, SwitzerlandE-mail: adolf.friedrich.fercher@univie.ac.atReceived 23 October 2002Published 20 January 2003Online at stacks.iop.org/RoPP/66/239AbstractThere have been three basic approaches to optical tomography since the early 1980s: diffractiontomography, diffuse optical tomography and optical coherence tomography (OCT). Opticaltechniques are of particular importance in the medical field, because these techniques promiseto be safe and cheap and, in addition, offer a therapeutic potential. Advances in OCT technologyhave made it possible to apply OCT in a wide variety of applications but medical applicationsare still dominating. Specific advantages of OCT are its high depth and transversal resolution,the fact, that its depth resolution is decoupled from transverse resolution, high probing depth inscattering media, contact-free and non-invasive operation, and the possibility to create variousfunction dependent image contrasting methods. This report presents the principles of OCTand the state of important OCT applications.OCT synthesises cross-sectional images from a series of laterally adjacent depth-scans.At present OCT is used in three different fields of optical imaging, in macroscopic imaging ofstructures which can be seen by the naked eye or using weak magnifications, in microscopicimaging using magnifications up to the classical limit of microscopic resolution and inendoscopic imaging, using low and medium magnification. First, OCT techniques, likethe reflectometry technique and the dual beam technique were based on time-domain lowcoherence interferometry depth-scans. Later, Fourier-domain techniques have been developedand led to new imaging schemes. Recently developed parallel OCT schemes eliminate the needfor lateral scanning and, therefore, dramatically increase the imaging rate. These schemes useCCD cameras and CMOS detector arrays as photodetectors. Video-rate three-dimensionalOCT pictures have been obtained. Modifying interference microscopy techniques has led tohigh-resolution optical coherence microscopy that achieved sub-micrometre resolution.This report is concluded with a short presentation of important OCT applications.Ophthalmology is, due to the transparent ocular structures, still the main field of OCTapplication. The first commercial instrument too has been introduced for ophthalmic0034-4885/03/020239 65 90.00 2003 IOP Publishing LtdPrinted in the UK239

240A F Fercher et aldiagnostics (Carl Zeiss Meditec AG). Advances in using near-infrared light, however, openedthe path for OCT imaging in strongly scattering tissues. Today, optical in vivo biopsy is oneof the most challenging fields of OCT application. High resolution, high penetration depth,and its potential for functional imaging attribute to OCT an optical biopsy quality, which canbe used to assess tissue and cell function and morphology in situ. OCT can already clarify therelevant architectural tissue morphology. For many diseases, however, including cancer in itsearly stages, higher resolution is necessary. New broad-bandwidth light sources, like photoniccrystal fibres and superfluorescent fibre sources, and new contrasting techniques, give accessto new sample properties and unmatched sensitivity and resolution.

Optical coherence tomography—principles and applications241Contents1. Introduction1.1. Basic schemes1.2. Mathematical treatment2. OCT signal properties2.1. Single scattering and optical tomography2.2. Multiple scattered sample light2.3. Probing depth2.4. Sensitivity2.5. Speckle2.5.1. Speckle properties2.5.2. Interferogram speckle2.5.3. Suppression of speckle in OCT2.6. Resolution2.6.1. OCT PSF and resolution2.6.2. Deconvolution2.6.3. Dispersion compensation2.6.4. Limited diffraction beams3. OCT light sources3.1. Coherence properties3.2. Wavelength3.3. Spectral structure3.3.1. Spectral width3.3.2. Spectral modulation3.3.3. Spectral phase4. Low-coherence interferometry and OCT4.1. Time-domain OCT4.1.1. Reflectometry OCT4.1.2. Dual beam OCT4.1.3. En-face OCT4.1.4. Heterodyne detection and delay lines4.2. Fourier-domain OCT4.2.1. Spectral interferometry Fourier-domain OCT4.2.2. Wavelength tuning Fourier-domain OCT4.3. Parallel OCT5. Functional OCT5.1. Polarization-sensitive OCT5.2. Doppler OCT5.2.1. Fourier-transforming the fringe data5.2.2. Sequential scan processing5.2.3. Fourier-domain 1271274275276277280282283284

2425.2.4. Hardware solutions5.3. Wavelength-dependent OCT5.3.1. Spectrometric OCT5.3.2. Fourier-domain SOCT5.3.3. Differential absorption OCT5.3.4. Coherence spectrotomography5.3.5. Refractometric OCT6. Applications of OCT6.1. OCT in ophthalmology6.2. Other medical fields: OCT biopsy and functional OCT6.2.1. High-resolution OCT in gastroenterology and dermatology6.2.2. Endoscopic OCT in intra-arterial imaging6.2.3. PS-OCT in dentistry6.2.4. Spectroscopic OCT in gastroenterology6.2.5. DOCT in haemostatic therapy6.3. Non-medical OCTAcknowledgmentsReferencesA F Fercher et 298298

Optical coherence tomography—principles and applications2431. IntroductionTomographic techniques generate slice images of three-dimensional objects. Opticaltomographic techniques are of particular importance in the medical field, becausethese techniques can provide non-invasive diagnostic images. There is a fundamentaldifference between optical tomography techniques and x-ray and magnetic resonancetechniques. Since optical techniques are dominated by diffraction the Fourier slice theoremcannot be used. There are two fundamental optical tomography techniques: diffuse opticaltomography (DOT), and optical diffraction tomography (ODT). Optical coherence tomography(OCT) is physically founded on ODT. The vast majority of applications of these techniques isin the biomedical field.DOT uses diffusely propagating photons. Spatially and/or temporally modulated lightis launched into the tissue and multiple scattered. Back-projection methods, perturbationmethods, and nonlinear optimization methods are used to derive tomographic images from thetransmitted light (Arridge and Schweiger 1997, Depeursinge 2002). ODT uses single scatteredlight and derives tomographic images by the Fourier diffraction projection theorem (Born andWolf 1999). Recently, it has been shown, that standard diffraction tomographic methods canalso be used for imaging with diffuse-photon density waves (Li et al 1997).OCT uses ballistic and near-ballistic photons. Laterally adjacent depth-scans (similarto the more familiar A-scans of ultrasound imaging technology) are used to obtain a twodimensional map of reflection sites in a sample. Initially, OCT techniques were based onlow time-coherence interferometry (LCI) depth-scans performed in the time domain. Ina first approach towards tomographic imaging a cross-sectional topographic image of theretinal pigment epithelium (RPE) of a human eye obtained in vivo by the dual beam LCItechnique was presented at the ICO-15 SAT conference by Fercher (1990) and published byHitzenberger (1991). OCT using fibre optic Michelson LCI was pioneered by Fujimoto andco-workers (Huang et al 1991). First in vivo tomograms of the human retina were publishedby Fercher et al (1993a) and Swanson et al (1993). Later Chinn et al (1997) used wavelengthtuning interferometry (WTI) to synthesize OCT images, whereas Häusler and Lindner (1998)generated OCT images using spectral interferometry. For a review of early work in LCI andOCT see the selection of key papers published by Masters (2001).1.1. Basic schemesFigure 1 depicts the standard OCT scheme. A low time-coherence light source is used in astandard Michelson interferometer. Note that there are basically two scan procedures in OCT:the OCT depth-scan is performed by the reference mirror. The lateral OCT scan is eitherperformed by moving the sample or by scanning the probe beam illuminating the sample.OCT synthesizes cross-sectional images from a series of adjacent LCI depth-scans. Incontrast to classical interferometry, LCI measures absolute distances. LCI is based on theoccurence of fringes if the optical path lengths of reference and sample beams coincide withinthe ‘coherence gate’, which is of the size of the so-called round trip coherence length lC :lC 2 ln 2 λ̄2,π λ(1.1)where λ̄ is the mean wavelength and λ the spectral width (Gaussian spectrum assumed;see section 4.1.1). For example, using a superluminescent light diode (SLD) as a low timecoherence light source and data from table 1 (λ̄ 820, λ 20 nm) yields a round tripcoherence length and thus depth resolution (see also section 2.6.1) of lC 15 µm.

244A F Fercher et alOCTDepthScanzReferenceBeamV(t) * (t)LateralOCTScanLSSourceBeamV(t)V(t) * h(x,t)SampleBeamDetectorBeamPCIE(x,z) IS IR 2Re[Γsource (z) h(x,z)]Figure 1. Standard OCT scheme based on a low time-coherence Michelson interferometer. Theintensity IE at the interferometer exit depends on the sample response h(x, z) convolved with thesource coherence function Source (z). LS low time-coherence light source; PC personalcomputer.OCT has, therefore, some outstanding properties: first of all, depth resolution is decoupledfrom transverse resolution. High depth resolution is possible even at sites not accessible by highnumerical aperture (NA) beams, like the fundus of the eye. If, however, high NA beams canbe used, high transversal resolution is obtained too; this technique is called optical coherencemicroscopy (OCM). Second, depth resolution in the histological 1 µm range is possible. Third,the interferometric technique provides high dynamic range and sensitivity ( 100 dB). Imagingof weakly scattering structures even in a scattering environment is possible, enabling ‘in situoptical biopsy’. Last, but not the least, it is important to note that in medical terms LCI andOCT are non-invasive techniques that yield in vivo data.At present, OCT uses exclusively time-coherence properties. There are, however, firstattempts towards space-coherence OCT. A corresponding technique using a space-coherencegate has recently been investigated by Rosen and Takeda (2000). These authors suggested thatthe spatial spectrum of the beam illuminating the object be varied by spatial masks in order touse the longitudinal component of the spatial coherence as a coherence gate for depth ranging.In a first demonstration Fresnel zone plate structures have been used to move the coherencegate. An advantage of this technique is that it is independent of the source spectrum. Thedisadvantage of the technique is, however, that depth resolution becomes dependent on theNA, as in classical imaging.Also, OCT uses exclusively linear optics at present. Two-photon interferometry, however,has just been shown to have the potential of still higher sensitivity, furthermore, to havethe potential of an enhancement of depth resolution by a factor of two, and of cancellationof dispersion. The two-photon interferometer makes use of a nonclassical entangled orcorrelated twin-photon light source. How far this so-called ‘quantum-OCT’ can replaceexisting linear interferometry techniques will largely depend on the practicability of thespontaneous parametric down-conversion light sources needed in that technique (Abouraddyet al 2002).

Optical coherence tomography—principles and applications2451.2. Mathematical treatmentIn this chapter we shall represent light waves as scalar, stationary, ergodic, random analyticsignals and follow the treatment given by Mandel and Wolf (1995). We shall also ignore fieldquantization and polarization (except in section 5.1) and use the following Fourier transform(FT) representation of the electric field E(t): Ê(ν) E(t) exp(2π iνt) dν FT{E(t)}(1.2) with the corresponding analytic signal Ê(ν) exp( 2π iνt) dν A(t) exp[i (t) 2π iν̄t],V (t) 2(1.3)0A(t) ei (t) is the complex envelope of V (t), A(t) V (t) the real envelope, and ν̄ the meanfrequency of the power spectrum of V (t). Furthermore, we define the instantaneous intensitybyI (t) V (t)V (t).(1.4)We shall furthermore describe interference phenomena of light waves as second-ordercorrelation phenomenona. The mutual coherence function of such light waves VS (samplewave) and VR (reference wave) is a second-order cross-correlation function, (1.5) SR (τ ) VS (t)VR (t τ ) ,where the angle brackets mean ensemble average. Since we are concerned with stationaryand ergodic waves, all ensemble averages are independent of the origin of time and may bereplaced by time-averages. The averaged intensity is the auto-correlation ACFV (τ ) at τ 0:(1.6)I I (t) V (t)V (t τ ) τ 0 ACFV (τ ) τ 0 (τ ) τ 0 .We shall make extensive use of the interference law: after introducing a time delay t, lightfrom a sample beam interferes with light from a reference beam at the interferometer exit(index E):VE (t; t) VS (t) VR (t t).(1.7)The averaged intensity at the interferometer exit is I E ( t) IE (t; t) EE (0; t) VE (t; t)VE (t; t) IS (t) IR (t) GSR ( t).(1.8)The interferogram GSR ( t) is twice the real part of the cross-correlation of the analytic signalsof the two interfering beams: GSR ( t) 2Re VS (t)VR (t t) 2Re{ SR ( t)} 2 IS (t) IR (t) γSR ( t) cos[αSR δSR ( t)].(1.9)γSR ( t) is the complex degree of coherence of the two waves, γSR ( t) is their degree ofcoherence; δSR ( t) 2π ν̄ t is the phase delay, t ( z/c) the time delay, z the pathdifference between the beams and c the speed of light. αSR is a constant phase.Since (τ ) is an analytic function it can be obtained from its real part G(τ ) 2Re{ V (t)V (t τ ) } by analytic continuation:i1(1.10) (τ ) G(τ ) HT{G(τ )},22where HT means Hilbert transform, and G(τ ) is obtained from the LCI signal.

246A F Fercher et alLCI and OCT are based on the photoelectric signal UG (t) of the interferogram GSR in alow-coherence interferometer (obtained by band-pass filtering of the photoelectric heterodyneinterferometer ac signal). Photodiodes are generally used as detectors as they can providenear-shot-noise limited operation in OCT configurations. The photodiode signal is measuredas current because of its better linearity, offset, and bandwidth performance compared tovoltage measurement. The generated photocurrent is proportional to the incident light powerand is converted to voltage using a transimpedance electronic amplifier circuit. We shall callUG (t), and, sometimes, just GSR , the ‘LCI signal’ or ‘OCT signal’: qe ηGSR (r, t) d2 r,(1.11)UG (t) iG (t) hν̄ Ar(r)iG (t) is the photoelectric current, qe the electronic charge, η the quantum efficiency of thedetector, h the Planck’s constant, ν̄ the mean optical frequency, and Ar(r) the sensitivedetector area. Frequently, the envelope of the LCI signal is generated by rectification ofthe photoelectric ac signal followed by low-pass filtering. Alternatively, amplitude and phase(or the corresponding quadrature components) of the photoelectric ac signal are determinedusing a lock-in amplifier.If the photodetector surface at the interferometer exit is coplanar with the wavefronts ofthe interfering beams, we haveGSR (r, t) GSR (t) iG (t)and obtain the real envelope of the coherence function SR (t) A (t) e A (t) 21 (GSR (t))2 (HT{GSR (t)})2and its phase from(1.12)i (t)from(1.13) HT{GSR (t)}.(1.14)GSR (t)Finally, we shall use the corresponding spectral relations; these are obtained with the help ofthe Wiener–Khintchine theorem. First, we note that the power spectrum of a light wave isobtained as the FT of its self-correlation: (t) arctanS(ν) FT{ (τ )}.(1.15)Furthermore, the cross-spectral density function of two waves (VS and VR ) is obtained as theFT of the cross-correlation function:WSR (ν) FT{ SR (τ )},(1.16)and the spectral interference law is obtained asS(ν; t) SS (ν) SR (ν) 2Re[WSR (ν)] cos(2π ν t),(1.17)with the interferometric time delay t.2. OCT signal properties2.1. Single scattering and optical tomographyUnscattered photons like x-rays and γ -rays have been used to obtain tomographic straight rayprojections for a long time. The mathematical problem of reconstructing a function from itsstraight ray projections has already been presented by Radon (1917). Its solution, the Fourierslice theorem, shows that some of the three-dimensional Fourier data of the object can beobtained from two-dimensional FTs of its projections. Because of its analogy to the Fourier

Optical coherence tomography—principles and applications247diffraction theorem (Wolf 1969), we shall have a closer look at this theorem: from the FT ofan object function F (x, y, z) (which, e.g. in x-ray computer tomography (CT) characterizesthe two-dimensional distribution of the linear x-ray attenuation coefficient), F̂ (u, v, w) FT{F (x, y, z)} F (x, y, z) exp[2π i(ux vy wz)] dx dy dz,(2.1)it follows readily, that the projection P (x, y) F (x, y, z) dz has the two-dimensional FT FTx,y {P (x, y)} F (x, y, z) dz exp[2π i(ux vy)] dx dy F̂ (u, v, 0).(2.2)Hence, slices of the three-dimensional Fourier data of the object can be obtained from a FT ofits two-dimensional projections. In the CT technique, a series of such projections at differentdirections is used to obtain depth resolution. To correct for the radial dependence of the Fourierdata density introduced by the projection procedure a filtering step is applied (Kak and Slaney1988).Optical tomography techniques and, in particular, OCT, deviate in several respects fromthat more known CT concept: (1) DOT uses highly diffracted and scattered radiation; straightray propagation can only be assumed for a fraction of the photons; the reconstruction algorithmmust take care of diffraction. (2) OCT images are synthesized from a series of adjacentinterferometric depth-scans performed by a straight propagating low-coherence probing beam;that leads to an advantageous decoupling of transversal resolution from depth resolution.(3) OCT uses backscattering; light propagates twice through the same object region.Figure 2 depicts two implementations of OCT. A rotating mirror is used to provide thelateral OCT scan. Note that, to implement the confocal scheme too (the core diameter ofsingle-mode fibres is approximately 5 µm) a pinhole is used in front of the photodetector inthe free-space optics scheme). Thus, light from outside the sample focus volume is suppressed.Let us consider a weakly inhomogeneous sample illuminated by the waist of an opticalGaussian probe beam. Hence, within a depth extension of the order of magnitude of theRayleigh length we can assume plane-wave illumination with incident waves:V (i) (r, k(i) , t) A(i) exp(ik(i) · r iωt),(2.3)k(i) is the wave vector of the illuminating wave, k(i) k 2π /λ the wave number. Then, using the outgoing free-space Green’s function GH (r, r ) (eik r r / r r ) ofthe Helmholtz operator, the first-order Born approximation yields the scattered wave as anapproximate solution of the Helmholtz equation (Wolf 1969, Born and Wolf 1999): 1VS (r, k(s) , t) V (i) (r, k(i) , t) V (i) (r , k(i) , t) · FS (r , k) · GH (r, r ) · d3 r .(2.4)4π Vol(r )k(s) is the wave vector of the scattered wave, k(s) k. This integral is extended over waveletsoriginating from the illuminated sample volume Vol(r ). The relative amplitudes of thesewavelets are determined by the scattering potential of the

INSTITUTE OF PHYSICS PUBLISHING REPORTS ON PROGRESS IN PHYSICS Rep. Prog. Phys. 66 (2003) 239–303 PII: S0034-4885(03)18703-9 Optical coherence tomography—principles and applications A F Fercher 1, W Drexler , C K Hitzenberger and T Lasser2 1 Institute of Medical Physics, University of Vienna, Waehringer Strasse 13, A-1090 Wien, Austria 2 Laboratoire d’optique biomedicale, Institut d .

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